The cytoplasm of a cell is a (moderately) conducting fluid, surrounded by an ins
ID: 560346 • Letter: T
Question
The cytoplasm of a cell is a (moderately) conducting fluid, surrounded by an insulating membrane, and embedded in a solution that is usually at least somewhat conducting. It can therefore be treated as a capacitor. Assume the cell is spherical with a radius r=10m, the cell membrane has an area A=4r2, and a thickness D 5nm. The capacitance should then be given by C=A/D, where the permittivity is given by r0 with r, the dielectric constant, having a value of approximately 5, and 0=8.8542×1012Fm1.
Part A
Calculate the capacitance of the cell membrane.
Express your answer to one significant figure.
______ Farad
Part B
Calculate how many unipositive ions need to cross the cell membrane to give the interior a potential of 100 mV.
Express your answer to one significant figure.
_________ unipostive ions
Explanation / Answer
A)
Area, A = pi*r^2
= 3.14*(10*10^-6 m)^2
= 3.14*10^-10 m^2
d = 5 nm = 5.0*10^-9 m
C = eo*A/d
= 8.8542*10^-12 * 3.14*10^-10 / 5.0*10^-9
= 5.56*10^-13 F
Answer: 6*10^-13 F
B)
use:
Q = C*V
= 5.56*10^-13 * 100*10^-3
= 5.56*10^-14 C
number of ion = Q / charge of 1 ion
= ( 5.56*10^-14 ) / (1.602*10^-19)
= 3.47*10^5
Answer: 3*10^5
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